Fellow Shashaank Vattikuti and I have been exploring how genetic and anatomical perturbations can give rise to conditions such as autism spectrum disorder and overeating. In particular, we used a local cortical circuit at the sub-millimetre level as a bridge between genotype and phenotype. We have found that synaptic imbalance and changes in the minicolumn structure of cortex can effect performance in visual saccade tasks that match experiments. The model also makes predictions for possible pharmacological therapeutics. We are now collaborating with Steve Gotts and Alex Martin to develop psychophysical tests to probe cortical circuit dynamics. One cognitive phenomenon that may be usefully exploited to probe cortical circuit function is binocular rivalry, where each eye is presented with a different image and the brain's perception alternates between the two images. For the past decade, I have been developing a cortical circuit model involving mutual inhibition that can explain much of the physiology of rivalry. However, recent work showed that the simple mutual inhibition model demonstrated a regime where dominance times decrease as the contrast of the images decreased contrary to experimental evidence. With former fellow Jeffrey Seely, we showed that this anamolous behavior could be eliminated in a mutual inhibition model with some simple biophysically plausible adjustments. Former fellow Phyllis Thangaraj, Vattikuti and I are extending the rivalry model to incorporate spatial dependence in what is known as the quartet illusion. We are also testing ASD and typical subjects on the quartet illusion to look for differences and to validate the model. When the visual field is present with two images the response of a neuron to the images is sub-additive compared to when the images are presented individually. This control of dynamic range is called normalization. Fellow Hua Xie and I are using machine learning methods to find biophysically plausible parameters for a cortical circuit model that matches the experimental data quantitatively. Most of the past work on the dynamics of interacting neurons or oscillators have focused on the infinite system size limit where fluctuations due to the connections do not appear. However, many biological and neural networks are large but finite sized. The dynamics of such networks are not well understood. Former fellow Michael Buice and I examined the dynamics of a large but finite size network of globally connected oscillators. The model is the weak coupling limit of a mutually connected network of neurons that have a tendency to synchronize due to the connections. We showed that ideas from the kinetic theory of gases and plasmas could be applied to analyze the fluctuations and correlations due to system size effects. In particular, we showed that finite population size could stabilize the marginal asynchronous mode. This had been an open problem for twenty years. We showed how to derive an effective stochastic equation for a neuron embedded in network of unmeasured neurons. We have also developed a scheme to generalize population rate equations to account for correlations. The approach shows how a moment hierarchy can be generated from an underlying Master equation. We have recently generalized this method to explicitly compute generalized population activity equations directly from a network of deterministic neurons.